Classical Eddy Current Loss Research Articles

High-Frequency Tunneling Magnetic Loss in Soft Ferrites

This paper considers high-frequency (200 kHz-1.0 MHz) losses in MnZn power ferrites and shows that none of the three well-known magnetic loss mechanisms (namely, hysteresis, classical eddy-current loss, and excess eddy-current loss) can account for the experimentally observed dependence of the loss on the frequency and flux density. In order to investigate the origin of this discrepancy, the electric field that is induced in the typical core when the material is driven at high frequencies and flux densities was estimated. The estimates show that these electric fields can be quite large. The paper presents experimental data on the electrical conductivity for such large electric fields, which shows a highly nonlinear behavior that can give rise to a modified eddy-current loss mechanism. By a simple curve fit to the nonlinear conductivity, the experimentally observed flux density dependence of the high-frequency loss, which previously could not be explained, can be reproduced by using this modified eddy-current loss mechanism. A modified ferrite structure can eliminate most of these extra losses by reducing the electric field generated at the grain boundaries due to high frequencies and flux densities

A Practical Circuit Model of High Frequency Transformers in Power Electronic Systems

AbtractThis paper presents a practical circuit model of high frequency transformers in power electronic systems. All types of core losses (ie. the hysteresis, classical eddy current and anomalous losses) are included in the model. the thermal effect on magnetic hysteresis, the skin effect of eddy currents in magnetic cores and the effect of stray capacitances are also considered. This model can therefore accurately predict the performance and core losses of transformers used in high frequency switching circuits. The practical methods for determining the circuit parameters are developed and presented in the paper, providing crucial benefit for practical applications. The developed model has been applied to simulate the performance of a 500 W transformer in a full bridge inverter operated with square waveform voltage excitation of 25 kHz. The simulations are validated by the experimental results.

Ｆｅ‐Ｓｉ系圧粉磁心の粉末粒径および結晶粒径と磁心損失との関係

Compressed cores made with Fe-Si alloys are expected for smoothing and boost choke coils of switching regulators and DC-DC converters. In this study, compressed cores were made with atomized Fe-3mass%Si, and the relationships between particle size, crystal grain size and core loss were investigated. The crystal grain sizes were changed by heat treatment temperature. The following conclusions were obtained. (1) Hysteresis loss decreases with increase in crystal grain size. (2) Both contributions of classical eddy current loss assuming uniform magnetization and localized eddy current loss by domain wall movements were confirmed. It was found that anomalous eddy current loss is proportional to square root of the crystal grain size. As particle size decreases, anomalous eddy current loss becomes dominant relative to classical eddy current loss, because classical eddy current loss decreases.

On a low-dimensional model for magnetostriction

In recent years, a low-dimensional model for thin magnetostrictive actuators that incorporated magneto-elastic coupling, inertial and damping effects, ferromagnetic hysteresis and classical eddy current losses was developed using energy–balance principles by Venkataraman and Krishnaprasad. This model, with the classical Preisach operator representing the hysteretic constitutive relation between the magnetic field and magnetization in the axial direction, proved to be very successful in capturing dynamic hysteresis effects with electrical inputs in the 0–50 Hz range and constant mechanical loading. However, it is well known that for soft ferromagnetic materials there exist excess losses in addition to the classical eddy current losses. In this work, we propose to extend the above mentioned model for a magnetostrictive rod actuator by including excess losses via a nonlinear resistive element in the actuator circuit. We then show existence and uniqueness of solutions for the proposed model for electrical voltage input in the space L 2 ( 0 , T ) ∩ L ∞ ( 0 , T ) and mechanical force input in the space L 2 ( 0 , T ) .

A viscous-type dynamic hysteresis model as a tool for loss separation in conducting ferromagnetic laminations

A viscous-type dynamic hysteresis model (DHM) that is compatible with any static hysteresis model is described. In contrast to existing dynamic models, the DHM is characterized by fixed desired properties over an infinite frequency range and provides the possibility of changing the shape of the steady-state hysteresis loop. The way the DHM is combined with Maxwell equations makes it possible for the first time to separate all three components of the total loss in conducting ferromagnetic laminations. These are the static hysteresis loss, classical eddy-current loss, and the excess loss treated as a dynamic hysteresis component. The study of their frequency dependencies opens a possibility of accurate iron loss prediction based on the loss separation principle.

Influence of geometry and wave shape on magnetic amorphous material

The magnetic performance of 0.03 mm thick Co-based and 0.026 mm thick Fe-based amorphous ribbon in toroidal and strip form was measured under sine and pulse width modulation (PWM) waveform conditions. The measured loss, at 100 Hz fundamental frequency and a peak flux density of 91% of the saturation of each material, was separated into classical eddy current, hysteresis and anomalous loss components and the effect of geometry and waveform on these loss components was analysed. The results in general show a dimensional and waveform dependence which is not so great as in electrical steels.

Nanostructured metallic cores with extremely low loss and controlled permeability

Magnetic anisotropy perpendicular to the ribbon axis was induced in nanocrystalline FeCuNbSiB ribbons by crystallization under tensile stress, and the relative permeability of the ribbon was approximately 250. Toroidal cores for a choke coil were prepared from the ribbons. The magnetic loss decreased with increasing the core diameter and it was found that deterioration of magnetic properties due to formation of a toroidal core was suppressed by making the core diameter larger than the critical diameter determined from the values of magnetostriction and induced anisotropy. As a result, toroidal cores-with extremely low loss were achieved. The permeability of the cores developed was kept constant up to 1 MHz and their magnetic loss was much smaller than the loss values reported previously for nanostructured and amorphous cores with low permeability. The measured magnetic loss agreed with the calculated classical eddy current loss. In addition, the permeability and magnetic loss were kept constant up to the dc bias field, being three times higher than that applicable to a ferrite cut core with the same permeability value.

High performance nanostructured cores for chock coils prepared by using creep-induced anisotropy

The permeability of an Fe–Cu–Nb–Si–B ribbon was controlled by creep-induced anisotropy, and a toroidal core for a choke coil was developed. The loss of the core was much smaller than that of a ferrite core and agreed with the classical eddy current loss. The DC-bias field applicable to it was approximately twice as large as that for the ferrite core.

Analysis of iron loss in interior permanent magnet synchronous motor over a wide-speed range of constant output power operation

The paper presents the analysis of iron loss in interior permanent magnet synchronous motor over a wide-speed range of constant output power operation. The analysis is based on finite element method and uses the information on local flux density variation in the motor components. The total iron loss is calculated by summing up separately the hysteresis, classical eddy current and excess losses for each element of discretization over one electrical cycle of magnetic field variation in all parts of motor iron. The results of iron loss calculation were compared with the results obtained from experiments on the actual machine.

Behavior of Core Loss in Nanocrystalline Fe73.5Cu1Nb3Si13.5B9 Alloy with High Br

In the ranges of f=1020000Hz and Bm=0.11.0T, the core loss has been measured for nanocrystalline Fe73.5Cu1Nb3Si13.5B9 alloy with high Br. The total power loss was decomposed into the sum of the classical eddy current loss, the hysteresis loss and the excess loss. The results show that the change of the total loss per cycle with frequency clearly shows a nonlinear behavior, which has been described in terms of Bertotti's statistical theory of loss. The frequency range examined can nearly be divided into two intervals, in which there exist two different describing ways.

Effect of silicon on the loss separation and permeability of laminated steels

The effect of silicon content in the range from 0.21 to 2.0 wt% on the ac and dc magnetic properties of laminated steels after box annealing at 800°C for 5 h measured at 1.0 and 1.5 T induction has been investigated. Because of the combined effect of the hot-rolled plate grain size and the slowing down of grain boundary movement by silicon, steel containing 1.26 wt% silicon content had a maximum grain diameter after box annealing. Besides steel containing 1.26 wt% silicon, the texture of laminated steels was improved with increasing silicon content. The electrical resistivity of laminated steels increased linearly with increasing silicon content. The ac core loss, apparent eddy current loss, and classical eddy current loss of laminated steels decreased with increasing silicon content at both inductions. Silicon improved the ac core loss, hysteresis loss, classical eddy current loss and apparent eddy current loss through the combined effects of grain coarsening, texture improvement and increasing electrical resistivity. At 1.0 T induction, the variation of the ac and dc permeability with respect to silicon content was similar to that of grain size. It is suggested that the effect of grain size on permeability is more pronounced than that of texture at low induction. On the other hand, at 1.5 T induction, the variation of the ac and dc permeability and magnetic flux density with respect to silicon content were similar to that of the texture component ( I/ I R) 200. It is suggested that the effect of texture on permeability and magnetic flux density is more significant than that of grain size at high induction.

A generalized dynamic circuit model of magnetic cores for low- and high-frequency applications. I. Theoretical calculation of the equivalent core loss resistance

This paper describes the theoretical calculation of the equivalent core loss resistance for a dynamic magnetic core loss model. The equivalent core loss resistance incorporates the effects of both the classical eddy current and anomalous losses. Derivation of a generalized nonlinear core loss resistance expression is presented. This new equivalent core loss resistance can be incorporated into a generalized dynamic magnetic core circuit model suitable for low and high frequency applications.

Modelling the effects of eddy current losses on frequency dependent hysteresis in electrically conducting media

In recent studies it has been shown how the effects of classical eddy current losses can be used to extend the quasi-static hysteresis model to account for the frequency dependence of hysteresis in electrically conducting media. This paper deals with the extension of the hysteresis model to include anomalous or excess losses. The instantaneous power loss due to eddy currents then consists of two terms, one of which depends on (dB/dt)/sup 2/ and the other one on (dB/dt)/sup 1.5/. The first term is the classical power loss and the second term, due to Bertotti, is the excess power loss. It is shown how these terms are incorporated into a time dependent hysteresis model. The main achievement is that a self-consistent model of hysteresis has been developed in which the quasi-static hysteresis curves are shown to be a limiting case of the more general frequency dependent model. >

Loss optimization for iron-rich metallic glasses

We optimized the losses in iron-rich metallic glasses by surface crystallization and by annealing in a field perpendicular to the ribbon surface. Both methods lead to a weak perpendicular anisotropy and rotational magnetization processes. The origin of surface crystallization could be traced to the effects of oxygen during quenching and annealing. While in surface crystallized samples the ratio between measured losses and classical eddy current losses was at best 6 at 2000 Hz (0.2 T), a much better behaviour could be achieved by field annealing. With careful sample preparation and annealing, a Ni-content of 2.5% proved to be sufficient to obtain low losses between 2-3 times the classical eddy current losses in a large range of magnetization amplitudes and frequencies at permeabilities in excess of 10000. Domain observations show uniform magnetization processes.

Low core loss rotating flux transformer

A rotating magnetic induction at saturation generates no hysteresis losses. In addition, because domain walls are absent, there are no anomalous eddy current losses. Thus, only classical eddy current losses are present. In materials with high resistivity such as ferrites or materials fabricated into thin sheets such as amorphous metals, these classical losses are small. A transformer has been designed which utilizes this principle. It consists of a hollow toroidal core with toroidal windings wrapped outside the core and poloidal windings wrapped through the interior channel. When these windings are energized by currents 90 electrical degrees apart or, with suitable winding schemes, by three-phase currents, rotating flux is generated throughout the core volume.

方向性けい素鋼板の磁気特性におよぼす板厚と張力の影響

In general, decrease in sheet thickness decreases the core loss due to the decreased classical eddy current loss. However, at small thickness, surface pinning effects on the domain wall movement become dominant. The proportion of anomalous eddy-current loss arising from the domain wall movement is as much as about 45% of the total loss at the commercial frequencies, 50 and 60 Hz, but the relationship between the anomalous loss and the sheet thickness has not been clarified yet. The tensile stress imparted by the inorganic coating decreases the core loss, but there is no evaluation of the effect of thickness with tensile stress on the core loss.The systematic investigation has been made on specimens with various sheet thickness, for which the chemical polishing technique has been used.The decrease in core loss with tensile stress was greater for smaller thickness. Especially, for B8=1.77 T, the applied tensile stress increased the core loss for larger thickness and decreased the core loss for smaller thickness. The greater tensile stress decreases the domain wall spacing. The decrease in domain wall spacing with tensile stress was greater for larger thickness than for smaller thickness.The magnetostriction measurements indicated that the 90° domain volume at a demagnetized state was smaller for smaller thickness, and the volume of new 90° domains created at intermediate inductions due to the need of reducing magnetostatic energy was smaller for smaller thickness. The applied stress decreased the 90° domain volume at a demagnetized state and suppressed the formation of 90° domains at intermediate inductions. The magnetostatic energy due to free poles appearing on the surface was less effective in reducing the domain wall spacing and creating 90° domains for smaller thickness.The decrease in core loss with stress was due mainly to the decreasing supplementaly domains, especially 90° domain volume. The behavior of magnetization for a smaller thickness sheet was similar to that for a larger thickness sheet with larger B8.

Separation of losses in oriented silicon steels from 0.13 to 0.34 mm thick

Regular grain oriented 3% silicon steels were produced by conventional techniques to final gages ranging from 0.13 to 0.34 mm thick. The steels were evaluated at frequencies from 20 to 60 Hz and at inductions from 1.0 to 1.7T. Core loss minima were observed at about 0.2 mm; scribing at 5 mm intervals transverse to the rolling direction removed the minima and resulted in monotonic reduction in loss to as low as 1.32 W/kg/60Hz/1.7T at 0.135 mm thickness. Hysteresis loss, coercive force and domain wall spacing increased as thickness was decreased below 0.20 mm, and overcame the reduction in classical eddy-current losses, resulting in the observed minima. Scribing reduced the domain wall spacing and consequently the synchronous and asynchronous eddy-current losses. Electropolished samples with no forsterite and very smooth surfaces had larger domain wall spacings than the above samples, but the hysteresis losses and the synchronous and asynchronous eddy-current losses were reduced so that core losses were as low as 1.1W/kg/60Hz/1.7T and, with the sample under 10.3 MPa uniaxial tension, were as low as 1.00 W/kg/60Hz/1.7T at 0.10 mm thickness. With improved texture (lower hysteresis loss) and domain refinement (lower eddy-current losses), at 0.10 mm thick, core losses below 0.76 W/kg/60Hz/1.7T (0.34 W/#/60Hz/1.7T) are achievable.

Effects of field annealing on the magnetic characteristics and magnetic losses of amorphous ribbons Fe78Si10B12

The effects of magnetic annealing on the magnetic characteristics and magnetic losses of amorphous ribbons Fe78Si10B12 were studied. The annealing temperature was chosen at 400°C, being lower than the Curie temperature 440°C. A magnetic field of 30 Oe was applied during the heat treatment, in a direction at an angle θ to the length of the ribbon, with θ = 0°, 45°, 60°, 90°. The magnetic characteristics in ac fields were measured with the frequencies from 50 Hz to 10 kHz. The total losses W were measured and resolved into the hysteresis loss Wh, the classical eddy current loss We, and the anomalous eddy current loss Wea. In general, at a given frequency and a given maximum induction, Wea decreases and Wh increases with the direction θ. So the optimum annealing conditions for lowest total loss are different for different frequency and maximum induction.

The causes of the anomalous loss in amorphous ribbon materials

The total power loss under alternating flux at power frequencies and zero applied stress conditions is an important criterion for the manufacturer and user of soft magnetic materials. The total power loss may be divided into three major types, namely the static hysteresis loss, classical eddy current loss and excess eddy current loss. It has been shown that the excess eddy current loss is responsible for approximately 90% and 50% of the total power loss of wide amorphous ribbon and grain-oriented silicon-iron respectively. Therefore it is possible to make comparisons of the causes and magnitude of the excess eddy current loss in these materials. The origin of the excess eddy current loss in grain-oriented 3% silicon-iron has been attributed to many causes. The feasibility of each of the suggestions as a possible cause of the excess eddy current loss of amorphous ribbon material is considered. It is concluded that the principal cause of the excess eddy current loss in amorphous ribbons is the non-sinusoidal non-uniform and non-repetitive domain wall motion which is the source of the observed non-sinusoidal and localised variations of the flux density.

Temperature dependence of power loss anomalies in directional FeSi 3%

Measurements as a function of temperature t were performed on directional FeSi 3%, in order to study the possible influence on the power loss anomalies of a change of intrinsic parameters, such as crystalline anisotropy energy K, without affecting the extrinsic ones, such as grain size and orientation. Power losses per cycle P/f were measured vs. frequency f, between d. c. and 50 Hz at various temperatures ranging from 25 to 650°C. The variation of K and of saturation induction B s with t were also determined up to the Curie point by means of a torque magnetometer. The results show that the excess loss anomaly at 50 Hz, measured by the ratio of experimental to classical eddy-current loss, and the non-linearity anomaly, determined from the renormalized P/f vs. f curves, are essentially independent of t. Analogies with the temperature dependence of the power density spectrum of the Barkhausen noise, which varies according to a B_{s}^{2} (t) law, are briefly discussed. These results seem to indirectly stress the role of extrinsic parameters in determining the anomalous loss behaviors in directional FeSi 3%. Kerr observations made up to 350°C on a (300 × 30)mm2strip did not detect any change of stripe domain widths and patterns.